The Category of Topological De Morgan Molecular Lattices

The concept of topological molecular lattices was introduced by Wang as a generalization of ordinary topological spaces, fuzzy topological spaces and L-fuzzy topological spaces in terms of closed elements, molecules, remote neighbourhoods and generalized order homomorphisms. In our previous work, we introduced the concept of generalized topological molecular lattices in terms of open elements and investigated some properties of them. In this paper, we dene and consider the category TDML whose objects are topological De Morgan molecular lattices and whose morphisms are continuous generalized order homomorphisms such that its right adjoins preserve the pseudocomplement operation. We show that this category is complete and cocomplete. In particular, we characterize products, coproducts, equalizers and coequalizers. Also, we show that the category TOP of all topological spaces is a re ective and core ective subcategory of TDML.